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"Krstajic has our confidence to lead the team in the coming period into the World Cup in Russia," Goran Bunjevcevic said, according to the agency Tanjug.
No details of the 43-year-old's contract were revealed. He will be officially unveiled in the second half of January, the FSS official added.
Krstajic had initially been named as an interim replacement for Slavoljub Muslin in October for the end of Serbia's successful World Cup qualifying campaign.
Krstajic played for Partizan Belgrade and spent almost a decade in Germany, with Werder Bremen and Schalke.
Muslin, 64, had taken over in May last year to succeed Radovan Curcic after Serbia's miserable showing in attempting to qualify for Euro 2016.
He steered them to first place in European qualifying Group D, ahead of the Republic of Ireland, Wales and Austria.
Serbia, who had not qualified for a major tournament since the 2010 World Cup, will face Brazil, Switzerland and Costa Rica in Group E in Russia.
